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Detlef Lohse - One of the best experts on this subject based on the ideXlab platform.
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exploring the phase diagram of fully turbulent taylor couette flow
Journal of Fluid Mechanics, 2014Co-Authors: Rodolfo Ostilla Monico, Erwin P Van Der Poel, Roberto Verzicco, Siegfried Grossmann, Detlef LohseAbstract:Direct numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently Rotating Cylinders, were performed. Shear Reynolds numbers of up to 3×10 5 , corresponding to Taylor numbers of Ta=4.6×10 10 , were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-Rotating and weakly counter-Rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-Rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-Rotating Cylinders, and that wider gaps behave like smaller gaps with weakly counter-Rotating Cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.
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exploring the phase diagram of fully turbulent taylor couette flow
arXiv: Fluid Dynamics, 2014Co-Authors: Rodolfo Ostilla Monico, Erwin P Van Der Poel, Roberto Verzicco, Siegfried Grossmann, Detlef LohseAbstract:Direct numerical simulations of Taylor-Couette flow (TC). Shear Reynolds numbers of up to $3\cdot10^5$, corresponding to Taylor numbers of $Ta=4.6\cdot10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios $\eta$, different aspect ratios $\Gamma$ and different rotation ratios $Ro$. It is shown that the transition is approximately independent of $Ro$ and $\Gamma$, but depends significantly on $\eta$. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-Rotating and weakly counter-Rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-Rotating regime where a mixture of stable and unstable regions exist. Furthermore, an analogy between $\eta$ and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-Rotating Cylinders, and that wider gaps behave like smaller gaps with weakly counter-Rotating Cylinders. Finally, the effect of $\Gamma$ on the effective torque versus $Ta$ scaling is analysed and it is shown that different branches of the torque-versus-$Ta$ relationships associated to different aspect ratios are found to cross within $15%$ of the $Re$ associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner vs outer $Re$ number parameter space and in the $Ta$ vs $Ro$ parameter space, which can be seen as the extension of the Andereck \emph{et al.} phase diagram towards the ultimate regime.
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The Twente turbulent Taylor-Couette (T3C) facility: strongly turbulent (multiphase) flow between two independently Rotating Cylinders.
Review of Scientific Instruments, 2011Co-Authors: Dennis P M Van Gils, Gert-wim Bruggert, Daniel P Lathrop, Detlef LohseAbstract:A new turbulent Taylor–Couette system consisting of two independently Rotating Cylinders has been constructed. The gap between the Cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 × 106 with water as working fluid. With this Taylor–Couette system, the parameter space (Rei, Reo, η) extends to (2.0 × 106, ±1.4 × 106, 0.716−0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor–Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness
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The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently Rotating Cylinders
The Review of scientific instruments, 2011Co-Authors: Dennis P. M. Van Gils, Gert-wim Bruggert, Daniel P Lathrop, Chao Sun, Detlef LohseAbstract:A new turbulent Taylor-Couette system consisting of two independently Rotating Cylinders has been constructed. The gap between the Cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 x 10^6 with water as working fluid. With this Taylor-Couette system, the parameter space (Re_i, Re_o, {\eta}) extends to (2.0 x 10^6, {\pm}1.4 x 10^6, 0.716-0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor-Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness.
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torque scaling in turbulent taylor couette flow between independently Rotating Cylinders
Journal of Fluid Mechanics, 2007Co-Authors: Bruno Eckhardt, Siegfried Grossmann, Detlef LohseAbstract:Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial Cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = u(r,,z,t)/r across the cylinder gap and and the excess energy dissipation rate w due to the turbulent, convective fluctuations (the ‘wind’) are derived and their dependence on the control parameters analysed. The very close correspondence of Taylor–Couette flow with thermal Rayleigh–Benard convection is elaborated, using these basic quantities and the exact relations among them to calculate the torque as a function of the rotation frequencies and the radius ratio η = r1/r2 or the gap width d = r2 − r1 between the Cylinders. A quantity σ corresponding to the Prandtl number in Rayleigh–Benard flow can be introduced, . In Taylor–Couette flow it characterizes the geometry, instead of material properties of the liquid as in Rayleigh–Benard flow. The analogue of the Rayleigh number is the Taylor number, defined as Ta (ω1 − ω2)2 times a specific geometrical factor. The experimental data show no pure power law, but the exponent α of the torque versus the rotation frequency ω1 depends on the driving frequency ω1. An explanation for the physical origin of the ω1-dependence of the measured local power-law exponents α(ω1) is put forward. Also, the dependence of the torque on the gap width η is discussed and, in particular its strong increase for η → 1.
Bruno Eckhardt - One of the best experts on this subject based on the ideXlab platform.
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intermittent boundary layers and torque maxima in taylor couette flow
Physical Review E, 2013Co-Authors: Hannes J Brauckmann, Bruno EckhardtAbstract:Turbulent Taylor-Couette flow between counter-Rotating Cylinders develops intermittently fluctuating boundary layers for sufficient counter-rotation. We demonstrate the phenomenon in direct numerical simulations for radius ratios ?=0.5 and 0.71 and propose a theoretical model for the critical value in the rotation ratio. Numerical results as well as experiments show that the onset of this intermittency coincides with the maximum in torque. The variations in torque correlate with the variations in mean Taylor vortex flow, which is first enhanced for weak counter-rotation and then is reduced as intermittency sets in. To support the model, we compare it to numerical results, to experiments at higher Reynolds numbers, and to Wendt's data.
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torque scaling in turbulent taylor couette flow between independently Rotating Cylinders
Journal of Fluid Mechanics, 2007Co-Authors: Bruno Eckhardt, Siegfried Grossmann, Detlef LohseAbstract:Turbulent Taylor–Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial Cylinders with radii r1 < r2 is analysed theoretically. The current Jω of the angular velocity ω(x,t) = u(r,,z,t)/r across the cylinder gap and and the excess energy dissipation rate w due to the turbulent, convective fluctuations (the ‘wind’) are derived and their dependence on the control parameters analysed. The very close correspondence of Taylor–Couette flow with thermal Rayleigh–Benard convection is elaborated, using these basic quantities and the exact relations among them to calculate the torque as a function of the rotation frequencies and the radius ratio η = r1/r2 or the gap width d = r2 − r1 between the Cylinders. A quantity σ corresponding to the Prandtl number in Rayleigh–Benard flow can be introduced, . In Taylor–Couette flow it characterizes the geometry, instead of material properties of the liquid as in Rayleigh–Benard flow. The analogue of the Rayleigh number is the Taylor number, defined as Ta (ω1 − ω2)2 times a specific geometrical factor. The experimental data show no pure power law, but the exponent α of the torque versus the rotation frequency ω1 depends on the driving frequency ω1. An explanation for the physical origin of the ω1-dependence of the measured local power-law exponents α(ω1) is put forward. Also, the dependence of the torque on the gap width η is discussed and, in particular its strong increase for η → 1.
Daniel P Lathrop - One of the best experts on this subject based on the ideXlab platform.
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The Twente turbulent Taylor-Couette (T3C) facility: strongly turbulent (multiphase) flow between two independently Rotating Cylinders.
Review of Scientific Instruments, 2011Co-Authors: Dennis P M Van Gils, Gert-wim Bruggert, Daniel P Lathrop, Detlef LohseAbstract:A new turbulent Taylor–Couette system consisting of two independently Rotating Cylinders has been constructed. The gap between the Cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 × 106 with water as working fluid. With this Taylor–Couette system, the parameter space (Rei, Reo, η) extends to (2.0 × 106, ±1.4 × 106, 0.716−0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor–Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness
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The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently Rotating Cylinders
The Review of scientific instruments, 2011Co-Authors: Dennis P. M. Van Gils, Gert-wim Bruggert, Daniel P Lathrop, Chao Sun, Detlef LohseAbstract:A new turbulent Taylor-Couette system consisting of two independently Rotating Cylinders has been constructed. The gap between the Cylinders has a height of 0.927 m, an inner radius of 0.200 m, and a variable outer radius (from 0.279 to 0.220 m). The maximum angular rotation rates of the inner and outer cylinder are 20 and 10 Hz, respectively, resulting in Reynolds numbers up to 3.4 x 10^6 with water as working fluid. With this Taylor-Couette system, the parameter space (Re_i, Re_o, {\eta}) extends to (2.0 x 10^6, {\pm}1.4 x 10^6, 0.716-0.909). The system is equipped with bubble injectors, temperature control, skin-friction drag sensors, and several local sensors for studying turbulent single-phase and two-phase flows. Inner cylinder load cells detect skin-friction drag via torque measurements. The clear acrylic outer cylinder allows the dynamics of the liquid flow and the dispersed phase (bubbles, particles, fibers, etc.) inside the gap to be investigated with specialized local sensors and nonintrusive optical imaging techniques. The system allows study of both Taylor-Couette flow in a high-Reynolds-number regime, and the mechanisms behind skin-friction drag alterations due to bubble injection, polymer injection, and surface hydrophobicity and roughness.
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turbulent flow between concentric Rotating Cylinders at large reynolds number
Physical Review Letters, 1992Co-Authors: Daniel P Lathrop, Jay Fineberg, Harry L SwinneyAbstract:Turbulent Taylor vortex flow is studied in experiments for Reynolds numbers ${10}^{3}$R${10}^{6}$. Simple scaling of the torque with Reynolds number is m/Inot observed for any range of R, although the characteristic time scales and the transport of passive scalars are found to scale with the global torque measurements. Above a nonhysteretic transition observed at R=1.3\ifmmode\times\else\texttimes\fi{}${10}^{4}$, the torque has a Reynolds number dependence similar to the drag observed in wall-bounded shear flows such as pipe flow and flow over a flat plate.
Christoph R Muller - One of the best experts on this subject based on the ideXlab platform.
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the parameters governing the coefficient of dispersion of cubes in Rotating Cylinders
Granular Matter, 2017Co-Authors: J.r. Third, Christoph R MullerAbstract:Axial dispersion of cubic particles in horizontal, Rotating Cylinders was investigated using discrete element modelling simulations. We found that, similar to the behavior of spheres, the axial dispersion coefficient of cubes depends on (1) the rotational speed of the cylinder \({\omega }\), (2) the acceleration due to gravity g and (3) the particle size d, satisfying the relationship \({D}_\mathrm {ax}\propto {\omega }^{1-2{\lambda }}{g}^{{\lambda }}{d}^{2-{\lambda }}\) with \({\lambda }\approx 0.15\) (\({\lambda }\approx 0.1\) for beds of spheres) (Third et al. in Powder Technol 203:510–517, 2010). This observation suggested that, although particle shape influences significantly the rate of axial dispersion (cubes disperse almost twice as fast as spheres of equal volume), the parameters controlling the coefficient of dispersion are independent of particle shape.
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axial dispersion of granular material in inclined Rotating Cylinders with bulk flow geometric model for 50 fill
Powder Technology, 2016Co-Authors: D. M. Scott, J.r. Third, Christoph R MullerAbstract:Abstract Monte Carlo particle tracking methods used to model particle motion in inclined Rotating Cylinders with bulk flow have been reported in the literature. This paper reports some analytic results for the mean squared deviation of axial position in the following special case: the particles are in the rolling mode; the bed surface is flat, with no axial variation of bed depth; the avalanche is instantaneous and of negligible thickness; collisional axial dispersion is ignored; fill = 0.5. Fill = 0.5 means that in every half-rotation of the cylinder every particle will have participated in one and only one avalanche; this simplification allows analytic results to be obtained. The calculations are carried out by relating the number densities of tracer particles in successive cycles of avalanching. In the case of well-mixed avalanches, the model is also developed using a random walk approach. The results confirm predictions obtained from discrete element modelling and Monte Carlo particle tracking simulations, which indicate that the mean squared deviation of axial position can oscillate with time for short enough times.
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is axial dispersion within Rotating Cylinders governed by the froude number
Physical Review E, 2012Co-Authors: J.r. Third, Christoph R MullerAbstract:Axial dispersion rates of particles within horizontal Rotating Cylinders have been calculated for a decade of cylinder diameters. Throughout the range studied the rate of axial dispersion was found to be independent of the cylinder diameter. This phenomenon has been investigated further by spatially resolving the local contribution to the axial dispersion coefficient. This analysis demonstrates that, although the highest rates of axial dispersion occur at the free surface of the bed, there is a significant contribution to axial dispersion throughout the flowing region of the bed. Finally, based on an analogy with a Galton board, a linear relationship is proposed between the local rate of axial dispersion within a horizontal Rotating cylinder and the product of the local particle concentration and the local shear rate in a plane perpendicular to the cylinder axis.
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tangential velocity profiles of granular material within horizontal Rotating Cylinders modelled using the dem
Granular Matter, 2010Co-Authors: J.r. Third, D. M. Scott, Stuart A Scott, Christoph R MullerAbstract:Flow regimes of granular materials in horizontal Rotating Cylinders are industrially important since they have a strong influence on the rates of heat and mass transfer within these systems. The tangential velocity profile, which describes how the average particle velocity in the direction parallel to the surface of the bed varies along a radius perpendicular to the surface of the bed, has been examined for many experimental and simulated systems. This paper is concerned with tangential velocity profiles within Rotating Cylinders simulated using the discrete element method. For high fill levels good agreement is found between the simulated velocity profiles and the equation proposed by Nakagawa et al. (Exp Fluids 16:54–60, 1993) based on magnetic resonance measurements. At lower fill levels slip is observed between the cylinder wall and the particles in contact with it and also between the outer layer of particles and the bulk of the bed. It is demonstrated that this slip occurs when the particles in contact with the wall are able to rotate and that it may be prevented either by using non-spherical particles or by attaching “lifters” to the cylinder wall.
J.r. Third - One of the best experts on this subject based on the ideXlab platform.
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the parameters governing the coefficient of dispersion of cubes in Rotating Cylinders
Granular Matter, 2017Co-Authors: J.r. Third, Christoph R MullerAbstract:Axial dispersion of cubic particles in horizontal, Rotating Cylinders was investigated using discrete element modelling simulations. We found that, similar to the behavior of spheres, the axial dispersion coefficient of cubes depends on (1) the rotational speed of the cylinder \({\omega }\), (2) the acceleration due to gravity g and (3) the particle size d, satisfying the relationship \({D}_\mathrm {ax}\propto {\omega }^{1-2{\lambda }}{g}^{{\lambda }}{d}^{2-{\lambda }}\) with \({\lambda }\approx 0.15\) (\({\lambda }\approx 0.1\) for beds of spheres) (Third et al. in Powder Technol 203:510–517, 2010). This observation suggested that, although particle shape influences significantly the rate of axial dispersion (cubes disperse almost twice as fast as spheres of equal volume), the parameters controlling the coefficient of dispersion are independent of particle shape.
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axial dispersion of granular material in inclined Rotating Cylinders with bulk flow geometric model for 50 fill
Powder Technology, 2016Co-Authors: D. M. Scott, J.r. Third, Christoph R MullerAbstract:Abstract Monte Carlo particle tracking methods used to model particle motion in inclined Rotating Cylinders with bulk flow have been reported in the literature. This paper reports some analytic results for the mean squared deviation of axial position in the following special case: the particles are in the rolling mode; the bed surface is flat, with no axial variation of bed depth; the avalanche is instantaneous and of negligible thickness; collisional axial dispersion is ignored; fill = 0.5. Fill = 0.5 means that in every half-rotation of the cylinder every particle will have participated in one and only one avalanche; this simplification allows analytic results to be obtained. The calculations are carried out by relating the number densities of tracer particles in successive cycles of avalanching. In the case of well-mixed avalanches, the model is also developed using a random walk approach. The results confirm predictions obtained from discrete element modelling and Monte Carlo particle tracking simulations, which indicate that the mean squared deviation of axial position can oscillate with time for short enough times.
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Modelling axial dispersion of granular material in inclined Rotating Cylinders with bulk flow
Granular Matter, 2015Co-Authors: J.r. Third, G. Lu, D. M. Scott, C.r. MullerAbstract:The axial dispersion of approximately monosized particles in rolling mode in Rotating Cylinders with bulk flow is examined using a Monte Carlo model and discrete element method (DEM) simulations. The Monte Carlo model predicts that the mean square displacement relative to the mean axial displacement of the bed undergoes oscillations in time. The nature of these oscillations depends on the fill level of the cylinder and the extent of particle mixing during avalanches. When the cylinder is half full the Monte Carlo model predicts undamped oscillations, whereas a filling fraction of 0.26 produces oscillations whose amplitude decreases with time. If mixing during avalanches is assumed to be perfect then the oscillations occur about a linear increase with time. In contrast, if it is assumed that the particles do not mix during avalanching, the oscillations occur about an increase with time which has a gradient which increases with time. There is good qualitative agreement between the Monte Carlo model with perfect mixing and the DEM when the filling fraction is 0.26. For a filling fraction of 0.5 the DEM data show oscillations about a faster than linear increase with time.
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is axial dispersion within Rotating Cylinders governed by the froude number
Physical Review E, 2012Co-Authors: J.r. Third, Christoph R MullerAbstract:Axial dispersion rates of particles within horizontal Rotating Cylinders have been calculated for a decade of cylinder diameters. Throughout the range studied the rate of axial dispersion was found to be independent of the cylinder diameter. This phenomenon has been investigated further by spatially resolving the local contribution to the axial dispersion coefficient. This analysis demonstrates that, although the highest rates of axial dispersion occur at the free surface of the bed, there is a significant contribution to axial dispersion throughout the flowing region of the bed. Finally, based on an analogy with a Galton board, a linear relationship is proposed between the local rate of axial dispersion within a horizontal Rotating cylinder and the product of the local particle concentration and the local shear rate in a plane perpendicular to the cylinder axis.
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axial dispersion of granular material in horizontal Rotating Cylinders
Powder Technology, 2010Co-Authors: J.r. Third, D. M. Scott, Stuart A ScottAbstract:The discrete element method is used to calculate axial dispersion coefficients for approximately monosized particles in a Rotating horizontal cylinder. Axial dispersion within the cylinder is shown to follow Fick's second law, in that the mean squared deviation of axial position of a pulse of particles is proportional to time. The axial dispersion coefficient is found to depend on the particle size, gravity and drum rotation speed, allowing a dimensionless group to be formed using these four quantities. For sufficiently large Cylinders, the axial dispersion coefficient is found to be independent of drum diameter. A general argument is given which suggests that axial dispersion in physical beds of approximately monosized particles should follow Fick's second law.
